Meaning at the Boundary

If all we have is a collection of text in a language we do not understand, can we derive its meaning?

Imagine a clay tablet covered in writing, sealed in a cave for three thousand years. No Rosetta Stone, no bilingual dictionary, no surviving speakers of the language. Just marks on clay. How much meaning could you possibly extract from it?

The surprising answer — one that runs from Claude Shannon’s information theory through modern AI and all the way to medieval Christian mysticism — is that the tablet contains far more than you’d think, and yet far less than it appears, and that the difference between those two things tells us something profound about what meaning actually is.

I. The Richness Inside the Text

Shannon, the father of information theory, estimated that English carries roughly 1.0 to 1.5 bits of entropy per character — far below the theoretical maximum of about 4.7 bits. The gap is redundancy, and redundancy is structure. Natural language is massively self-constraining. Every word narrows what can plausibly come next. Every sentence builds expectations about sentences to follow. That structure isn’t noise — it’s the skeleton of meaning.

Given enough text on our hypothetical tablet, a patient analyst could recover an extraordinary amount:

• The writing system itself. Character frequencies, word boundaries, the basic units of the language.

• Grammar. Word order rules, agreement patterns, how the language builds complex expressions from simple ones.

• Semantic relationships. Words that appear in similar contexts are “about” similar things. If the tablet uses one word near “throne,” “rule,” and “command,” and another word near “plow,” “harvest,” and “grain,” you’ve recovered something real about the conceptual world of the text — even without knowing what any of these words refer to.

• Logical and narrative structure. Questions posed early and answered late. Arguments built across paragraphs. Causal claims. Evaluative stances.

All of this emerges from nothing but the internal statistics of the text. No dictionary. No informant. No images. Just the patterns of co-occurrence among symbols.

This sounds like a theoretical curiosity until you realize that it’s exactly what a large language model does. Take a massive corpus of text — our tablet scaled up to billions of pages — and train a model to predict what comes next. What emerges is a system that can carry on coherent conversations, write poetry, reason about logic puzzles, explain quantum mechanics, and argue philosophy. All of it derived from the statistical structure of text, with no direct experience of the world the text describes.

The linguist J.R. Firth said in 1957: “You shall know a word by the company it keeps.” He meant it as a methodological principle. He didn’t know it was a blueprint for artificial intelligence.

II. The Gap: What’s Missing

But something crucial is absent. The language model “knows” that balls fall when dropped — this is a robust statistical regularity across millions of texts. But it has never seen a ball. It has never felt gravity. It has never experienced the arc of a falling object. Its knowledge is entirely relational: “fall” is what happens to “ball” in the context of “drop,” which relates to “gravity,” which connects to “force” and “mass” and “acceleration.” It’s an intricate web of associations, internally consistent and remarkably useful — but floating free of the world, untethered to anything outside itself.

This is the symbol grounding problem, and philosophers have been arguing about it for decades. A dictionary defines every word in terms of other words. At no point does the chain of definitions reach out and touch reality. The map is made entirely of more map.

For a long time, this seemed like a fatal limitation. How could a system that only knows relationships between symbols ever truly understand anything?

III. Closing the Loop

Then something interesting happened. We gave the language models tools.

Consider what happens when an AI assistant executes a command like ls on a filesystem. It emits a string of characters. Something happens outside the text — a real computer queries a real filesystem with real state. A result comes back that the model didn’t generate and couldn’t have fully predicted. For the first time, the model is in a perception-action loop. It acts, the world responds, and the response carries information that originated not from the statistics of language but from the actual state of an external system.

And the model can be wrong in a checkable way. It predicts a file exists. It runs ls. The file isn’t there. That discrepancy isn’t a disagreement about language — it’s a disagreement with reality. The model adjusts. It tries something else.

This is grounding. Not in the grand philosophical sense of “solving the problem of reference,” but in the practical, operational sense: the model’s internal representations are being calibrated against something outside itself.

The filesystem is a small world, but it has real structure. It has persistent state — files stay where you put them. It has causal logic — mv a file from one directory to another and it disappears from the first and appears in the second. It has failure modes — try to write to a read-only directory and you get an error that reflects a genuine constraint. The model, armed with its vast relational understanding of what these commands mean in the linguistic sense, now gets to test that understanding against a system that pushes back.

And this isn’t unique to filesystems. A web API is a window into the state of the world. A database query returns facts about real entities. A code execution environment lets the model write a program, run it, and observe whether the output matches its predictions. Each tool is another interface point, another channel through which reality can correct the model’s beliefs.

IV. Grounding as Alignment

Here’s where the picture simplifies dramatically. We’ve been treating grounding as a deep mystery — a philosophical puzzle about how symbols hook onto reality. But strip away the mystification and grounding is just alignment between systems.

You have an internal model. There’s something outside you. Grounding is the process of bringing those into correspondence. That’s it.

A toddler hears the word “ball” while a round thing rolls across the floor. She hears it again at the park, again in a picture book. Each time, she is doing the alignment work — noticing the correspondence between a sound and a perceptual category, testing it (”ball?” she says, pointing at an apple), getting corrected, and updating. No one can do this for her. The grounding happens because she is in the loop, making predictions and calibrating against feedback.

The language model with shell access is grounded relative to the filesystem. A human being is grounded relative to their sensory environment. A physical theory is grounded relative to experimental observation. In every case, the structure is identical: two systems in a relationship where each constrains the other, each informs the other, each provides the other with something it couldn’t generate alone.

Grounding isn’t binary. It’s not something you either have or don’t. It’s a spectrum of coupling tightness. The LLM trained only on text is loosely coupled to the world — it inherits grounding indirectly, through the residue of embodied authors who were tightly coupled. Give it tools, and the coupling tightens. Give it cameras and robotic arms, and it tightens further. At no point is there a magic threshold where “mere correlation” transforms into “true understanding.” There’s just more or less alignment, more or fewer interface points, tighter or looser feedback loops.

V. Meaning Is a Boundary Phenomenon

And now the insight that changes everything: meaning is just this relationship of alignment. Nothing more.

The word “ball” means something because it sits at the interface between the linguistic system and the perceptual system. It’s a point of correspondence between two different ways of carving up the world. The concept of “gravity” means something because it sits at the interface between a mathematical formalism and a set of physical observations. A stock price means something because it sits at the interface between a number on a screen and the real-world dynamics of supply, demand, and collective human behavior.

Meaning doesn’t reside inside any system. It lives between systems. It’s a property of the boundary, the interface, the relationship.

You can verify this with a simple thought experiment. Take one of the two systems away and meaning vanishes. A language with no speakers, no readers, no world to refer to — the tablet alone in a void — is just a pattern. A world with no one to describe it, model it, or categorize it has no “meaning” — it just is. Meaning requires both sides: something to represent and something to do the representing.

But here’s the truly surprising part. Try the opposite: instead of removing one system, merge them. Take the linguistic system and the perceptual system and treat them as a single unified system. What happens to the “meaning” of the word “ball”?

It disappears.

Not because anything was destroyed, but because meaning is a relationship between systems, and when you merge two systems into one, the relationship becomes an internal correlation. The word “ball” and the perception of a ball are now just two patterns within the same system, no more “meaningful” than the fact that one gear turns when another does. They co-occur. They’re correlated. But there’s no interface anymore, no boundary, no alignment between — just structure within.

This is why “what does the universe mean?” is such a bewildering question. If the universe is everything — one system with nothing outside it — then there’s nothing for it to be in correspondence with. Meaning, which requires an outside, has nowhere to live. The question doesn’t have a bad answer. It dissolves.

Appendix: Foundations, Meaning, and What Reaches Back

The main essay argues that meaning is alignment between systems — it lives at the boundary where one system meets another. But there is a related phenomenon that looks similar and isn’t, and the difference turns out to be revealing.

Axioms as foundation, not meaning. A mathematical theorem is grounded relative to the axioms it’s derived from. A conjecture floats free — it might be true, might be false. A proof anchors it: it shows that the proposition follows from the axioms, that the axioms demand it. The axioms give the system a place to stand.

But they don’t give it meaning.

The axioms are statements in the same language as the theorems. They’re not outside the system. They give math internal coherence — a foundation — but coherence isn’t meaning. Math gets meaning when it encounters something outside itself: when equations align with the motion of planets, when geometry maps onto actual space, when counting corresponds to actual sheep. The axioms make the system consistent. The encounter with the world makes it meaningful.

Where do the axioms themselves come from? Sometimes from physical intuition — Euclid’s postulates abstract from experience with straight edges and compasses. Sometimes from pragmatic choice. Sometimes from a sense of self-evidence that resists further analysis. And Gödel proved that any sufficiently rich formal system cannot prove its own consistency from within. The foundation is always, in some irreducible sense, imported from elsewhere — from a larger system, from intuition, from an act of trust. The system cannot justify the ground it stands on.

Values as foundation, not meaning. The same distinction holds for ethics. “Cruelty is wrong” grounds your moral reasoning. It gives you a place to stand, a foundation from which to derive judgments and principles. But the value itself doesn’t confer meaning on your moral life. Meaning arrives when your ethical framework meets actual lived experience — a real choice, a real consequence, a real person in front of you who is suffering. The value gives you a foundation. The encounter gives you meaning.

And the same Gödelian pattern holds. Try to ground your values in more fundamental values and you get infinite regress. Try to ground them in facts and you’ve crossed Hume’s guillotine — you’ve smuggled in an “ought” somewhere. The system of moral reasoning, like the formal system, cannot justify its own foundation from within.

So grounding and meaning are two different things. Grounding gives a system its foundation — the thing it stands on but cannot derive. Meaning is what happens when a system encounters something outside itself. One is internal. The other is relational.

When the foundation reaches back. But there are experiences that refuse this tidy separation. Consider what happens when you love someone.

You did not, strictly speaking, choose to love them the way you choose an axiom or commit to a value. It’s not a proposition you hold. It’s something you found yourself already inside of. And yet it organizes everything — your priorities, your fears, what gets you out of bed, what keeps you up at night. It functions as a foundation. But unlike an axiom, it isn’t inert. It isn’t something you posited and now stand on. It’s alive. It reaches back. The person you love is irreducibly outside you, beyond your control, beyond your full understanding — and your encounter with them is simultaneously the ground of your life and the thing that gives it meaning. Foundation and meaning, collapsed into a single experience.

Or consider the moment a piece of work suddenly meets you — when a problem you’ve been wrestling with opens up and you see it clearly. There’s a quality of being encountered, of being met by something outside yourself that you didn’t manufacture. Scientists describe this. Artists describe this. Parents watching their child become a person they didn’t design describe this. The common thread is the collapse of the distinction between what you stand on and what stands outside you. You are grounded by the encounter.

This is the experience Eckhart was trying to describe. Not a doctrine. Not a theological position. The lived experience of being a finite system that is met, held, and sustained by something beyond itself — something that can’t be derived, can’t be proved, and can’t be reduced to a commitment you made. He called it the Ground, and he said it overflows. It reaches toward you even as you reach toward it. It isn’t an assumption you make to get the system started. It’s the source from which the system perpetually arises.

Gödel showed that formal systems rest on something they can’t justify from within. Eckhart went further: that foundation isn’t just unjustifiable. It’s alive. And you don’t have to call it anything in particular to have felt it.

It may not be a coincidence that the deepest formal system humans have devised, the most ancient questions of how to live, and the most persistent human experiences of meaning all point, at their own foundations, to something they cannot formalize, cannot derive, and cannot do without.